Estimating the dimension of Thurston spine

Olivier Mathieu

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arXiv · 2310.15618

Estimating the dimension of Thurston spine

Olivier Mathieu

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Abstract

For g at least 2, the Thurston spine Pg is the subspace of Teichmueller space Tg , consisting of the marked surfaces for which the set of shortest curves, the systoles, cuts the surface into polygons. Our main result is the existence of an infinite set A of integers such that codim Pg is a o(g/ log g), when g varies over A. This proves the recent conjecture of M. Fortier Bourque.

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Olivier Mathieu. 2023-10-24. Estimating the dimension of Thurston spine. https://arxiv.org/abs/2310.15618

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